A conference-proceedings reminder that the non-Hermitian
one-dimensional complex Hamiltonians (such that $H^\dagger = PH P$
where $P$ is parity) admit not only the ``new" interpretation
(offered by the so called PT-symmetric Quantum Mechanics and
mediated, in essence, by the construction of the so called charge
operator $C$) but also the ``old" or ``standard textbook"
interpretation using trivial $C=P$ and treating any
positive/negative imaginary component of the potential simply as a
source/sink, respectively.


MR2109648
Weigert, Stefan . The physical interpretation of $PT$-invariant potentials.
Czechoslovak J. Phys. 54 (2004), no. 10, 1139--1142.